Transmission Electron Microscopy of Nanostructures

Transmission Electron Microscopy of Nanostructures

Chapter 4 Transmission Electron Microscopy of Nanostructures Thomas Walther University of Sheffield, Sheffield, England, United Kingdom CHAPTER OUTL...

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Chapter

4

Transmission Electron Microscopy of Nanostructures Thomas Walther

University of Sheffield, Sheffield, England, United Kingdom

CHAPTER OUTLINE

4.1 Introduction: Specimen Preparation for Electron Transparency 4.2 Transmission Electron Microscope Instrumentation 107 4.3 Electron Microscopy Methods 109 4.3.1 Diffraction Methods

106

109

4.3.1.1 Selected-Area Electron Diffraction With Parallel Illumination 109 4.3.1.2 Convergent-Beam Electron Diffraction 110

4.3.2 Imaging Methods 4.3.2.1 4.3.2.2 4.3.2.3 4.3.2.4 4.3.2.5 4.3.2.6

110

Bright- and Dark-Field Imaging 110 Weak-Beam Dark-Field Imaging 112 High-Resolution Electron Microscopy 113 Electron Holography 114 Energy-Filtered Transmission Electron Microscopy 117 Annular Dark-Field and Annular Bright-Field Scanning Transmission Electron Microscopy 118

4.3.3 Spectroscopy Methods

120

4.3.3.1 Energy-Dispersive X-ray Spectroscopy 120 4.3.3.2 Electron Energy-Loss Spectroscopy 122 4.3.3.3 Cathodoluminescence Spectroscopy 125

4.4 Applications to Nanostructures 4.4.1 4.4.2 4.4.3 4.4.4

125

Defects in Bulk Materials 125 Thin Films and Quantum Wells 126 Nanowires 127 The Problem of Reliable Size Measurements of Nanoparticles and Quantum Dots in Transmission 128

4.5 Tomography and the Projection Problem 4.6 Summary 130 References 130

130

Microscopy Methods in Nanomaterials Characterization. http://dx.doi.org/10.1016/B978-0-323-46141-2.00004-3 Copyright © 2017 Elsevier Inc. All rights reserved.

105

106 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

4.1 INTRODUCTION: SPECIMEN PREPARATION FOR ELECTRON TRANSPARENCY Transmission electron microscopy (TEM) comprises all forms of diffraction, imaging, or spectroscopy performed with high-energy electrons in transmission geometry. As the interaction of matter with electrons is very strong, multiple elastic and inelastic scattering of electrons by atoms are both very likely and imply that suitable specimens need to be very thin, usually below 100 nm in thickness, to achieve good signal-to-noise ratio and sufficient contrast in transmission. Most specimen holders are designed to receive and clamp in place 3-mm diameter disk specimens of up to 0.1 mm in maximum thickness in which only suitable edges of holes near their centers are examined. Depending on the type of material investigated, different methods to achieve electron transparency are typically used: n

n

n

n n

n

n

n

soft bulk matter (polymers) can be cut by ultramicrotomes, down to w30 nm in thickness; conductive bulk material (metals, alloys) can be electropolished or chemically etched to perforation; semiconductor and ceramic bulk specimens or thin films can be cut, ground, polished, and finally ion milled; some semiconductor specimens can be cleaved; flakes, fibers, nanowires, and other needle-shaped specimens, e.g., mineral fibers, can, if several micrometers in length, be directly dispersed on suitable metallic grids with very fine meshes; nanoparticles of any type can be dispersed, either as dry fine powders or from solutions using syringes or micropipettes, onto holey carbon films supported by metallic grids; for test and alignment purposes, metal alloys can be sputtered onto such holey carbon films supported by metallic grids; and bulk and thin film materials, as well as complete microdevices that cannot be easily handled otherwise, can be cut by a focused ion beam (FIB) instrument, which allows the user to prepare electron-transparent lamellae with parallel surfaces or needles. These can either be lifted out with the help of micromanipulators and placed onto holey carbon film samples for support (“ex situ” lift-out [1,2]) or they can be welded onto metallic support grids if a gas-injection system is available that can deposit C, Pt, or W (“in situ” lift-out [3]). Such FIB preparation is fast and efficient but tends to produce significant surface damage due to ion implantation that can be somewhat reduced by low-energy operation but cannot be avoided [4].

4.2 Transmission Electron Microscope Instrumentation 107

It is essential to think about optimal specimen preparation in advance, taking into account the criteria of effort, cost, possible specimen damage, and artifacts possibly due to the support by carbon films and metallic grids. The latter ones are usually prone to the fluorescence of unwanted stray X-rays if hit by high-energy electrons, primary X-rays generated by the specimen, or secondary X-rays from the pole pieces and apertures of the microscope, which complicates X-ray spectral interpretation. A detailed description of modern specimen preparation techniques can be found in the recent textbook by Ayache et al. [5], whereas classical recipes for chemical etching and electropolishing solutions for many materials are listed in the older volume by Thompson-Russell and Edington [6].

4.2 TRANSMISSION ELECTRON MICROSCOPE INSTRUMENTATION All transmission electron microscopes consist of an electron-emitting source, a linear accelerator, a two- or three-stage condenser lens system with condenser aperture to illuminate a specific part of the specimen, the specimen holder, the objective lens forming a magnified image, an objective aperture to restrict electrons to certain angles, a multiple-lens projector system to enhance magnification step by step, a selected-area aperture strip to choose where diffraction information comes from, and, finally, a twodimensional electron detector. Scanning transmission electron microscopes, in addition, have deflection coils above the specimen to scan a focused electron probe across the specimen, a corresponding set of descan coils below the specimen, and various detectors that can act as picoammeters over certain angular ranges. Different materials can be used as electron-emitting cathodes. In order of increasing brightness, cost, and vacuum demands, these are tungsten (W) hair-pin cathodes heated to >2000K (rare nowadays and mainly used in cheaper scanning electron microscopes), lanthanum hexaboride (LaB6) or cerium hexaboride (CeB6) cathodes heated to about 1800K, zirconia (ZrO2)-covered W tips simultaneously heated to w1500K and subjected to field emission (so-called Schottky electron guns) and cold (i.e., room temperature) W field emitters. Heating increases the probability of electron emission (i.e., current) and stabilizes the current; fieldemission relies on the quantum mechanical tunneling of electrons through surface states if subjected to high electric fields of the order of several volts per meter and delivers much higher brightness from a smaller point source. The linear accelerator consists of several anodes with pinholes through which an electron beam can be successively accelerated to typically 80e300 keV in energy. There are also a few instruments that can be run

108 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

at lower voltages, down to 30 kV [7], 20 keV [8], or even 5 kV [9] (to reduce knock-on damage and/or improve spectroscopy performance), or much higher voltages of 1e3 MeV [10] (to increase penetration power for much thicker specimens). The condenser consists of several electromagnetic lenses used to adjust illumination angle, area, and intensity independently, and it includes an aperture to restrict the angular range of illumination. The objective consists of a pair of very strong electromagnetic lenses with extended conical pole pieces that form a narrow gap of several (typically 2e10) millimeters into which the specimen holder can be inserted (“immersion lens” means that the specimen sits in the region of a saturated magnetic field) as well as a cold finger (to reduce contamination), the objective aperture strip, and sometimes further detectors (e.g., for X-rays). The objective lenses have a short focal length and produce a diffraction pattern in the back focal plane. Depending on the setting of the first projector lens (sometimes referred to as “diffraction lens”), either an image or a diffraction pattern is selected for further magnification step by step. If a diffraction pattern is to be studied, a selected area aperture blade in a conjugated image plane allows the user to select a small region (given by the pinhole diameter divided by the total magnification reached up to that point) that contributes to the diffracted intensity. Typical apertures of several 10 micrometers in physical size can yield diffraction patterns from areas as small as a few 10 nanometers (due to the magnification of the image with respect to the aperture plane). Two-dimensional detectors to record images or diffraction patterns usually first convert the primary (fast) electrons into light using a phosphorescent coating on a screen. This intensity pattern can then be viewed by the human eye or be transferred via fiber-optical coupling onto a digital charge-coupled device (CCD) detector that converts the light back into electrical charge amounts that can be measured. Recently, direct electron detectors based on complementary metaleoxideesemiconductor (CMOS) technology have also become available that can directly convert fast primary electrons into slow secondary electrons; however, such detectors for TEM need to be made radiation hard and back-thinned to expose the thinned silicon toward the electrons, facing all the sensitive electronics away from the direct beam. Alternative digital detectors can be simple arrays of photodiodes (then, again, usually fiber coupled to a scintillator) whereas negative plates or imaging plates are still used as traditional analog detectors, the intensity distribution of which can subsequently be converted into large-array digital images by appropriate scanners and calculation of the optical density.

4.3 Electron Microscopy Methods 109

For scanning TEM (STEM), the beam raster scans the specimen surface and images are maps computed from signals recorded at each pixel for a certain dwell time. Signals that can be recorded comprise electron intensities on axis (bright field) or off-axis (annular dark field), characteristic X-rays (energy-dispersive X-ray spectroscopy), energy losses (electron energyloss spectroscopy), or visible light (cathodoluminescence spectroscopy). Textbooks, e.g., [11,12], and often also the manufacturer manuals provide detailed descriptions of lens systems, aperture positions, and ray diagrams for the different imaging and diffraction modes.

4.3 ELECTRON MICROSCOPY METHODS 4.3.1 Diffraction Methods 4.3.1.1 Selected-Area Electron Diffraction With Parallel Illumination In this mode, the objective aperture is first focused by the diffraction lens adjustment to ensure the diffraction pattern produced is focused, then the objective aperture is retracted and the selected-area aperture is inserted. The result is a sharp diffraction spot pattern from the region selected. This can be used to check whether a specimen area is amorphous, polycrystalline, or single crystalline, cf. Fig. 4.1. If the sample is crystalline, the distances of the diffraction spots from the origin jjghkljj can be used to determine the corresponding planar spacings dhkl ¼ 1/jjghkljj from Bragg’s law: 2dhkl sin q ¼

n l

(4.1)

in which sin q denotes the Bragg angle of diffraction, n ¼ 1 the order of diffraction, and l the electron wavelength. One should be aware of lens

(A)

(B)

(C)

n FIGURE 4.1 Selected-area electron diffraction patterns of (A) single-crystalline silicon viewed along <110>, (B) textured metal (spots) with amorphous film on top (rings), and (C) polycrystalline NiMnGa film.

110 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

hysteresis and distortions, which mean that absolute measurements are hardly accurate to better than 1% and angles cannot be measured to better than 1 degree unless information from a suitable reference material is recorded simultaneously (i.e., superimposed on the same diffraction pattern). This restricts the determination of space groups and crystal orientations for which it is often vital to ensure that right angles can be identified with high confidence (if one of the three angles is, e.g., not 90 degrees but 89.8 degrees, then the crystal lattice is no longer orthorhombic but monoclinic).

4.3.1.2 Convergent-Beam Electron Diffraction If the parallel electron beam is defocused or the specimen taken off the correct (“eucentric”) height, then the diffraction spots are broadened into disks the radii for which correspond to the semiangle of beam convergence. Although these disks are featureless for very thin-foil specimens, thicker specimens produce a characteristic fringe pattern of so-called excess and deficiency lines, the spacings and positions of which contain information on crystal symmetry and thickness. These line patterns can be regarded as interference patterns from strongly diffracted beams and become the more detailed the thicker the specimen becomes. They allow the microscopist to determine symmetry elements of the crystal imaged, into which the textbook by Tanaka and Terauchi [13] gives an excellent introduction. In addition, at very large thicknesses, Kikuchi lines appear, as in Fig. 4.2B and C.

4.3.2 Imaging Methods 4.3.2.1 Bright- and Dark-Field Imaging For conventional imaging, an objective aperture must be chosen. A small pinhole centered on the optic axis produces a bright-field image, the contrast

(A)

(B)

(C)

n FIGURE 4.2 Convergent-beam electron diffraction of silicon along <001> zone axis at different thicknesses of (A) 0.46, (B) 2.0, and (C) 5.7 times the in-

elastic mean free path, L, at 300 kV.

4.3 Electron Microscopy Methods 111

of which for crystalline specimens depends mainly on diffraction condition (i.e., crystal orientation) and also somewhat on mass-thickness of the specimen (i.e., scattering power and number of atoms). For amorphous objects, the contrast stems almost exclusively from the mass-thickness product. Regions without specimen are uniformly bright (100% intensity). A small pinhole selecting exactly one diffracted beam produces a dark-field image, the contrast for which almost exclusively depends on the orientation and thickness of the crystal. Regions without specimen are uniformly dark (ideally 0%, but be aware that sometimes hardly visible support films create some stray intensity). It is common practice to avoid centering the objective aperture onto an off-axis reflection (as in Fig. 4.3B), which would increase lens aberrations. Instead, the objective aperture remains in place and the incident electron beam is tilted (by twice the Bragg angle!) until the desired Bragg reflection is on axis, as depicted in Fig. 4.3C. The spatial resolution is dictated by the diffraction limit: ddiff ¼

0:61b l

(4.2)

in which b is the semiangle (radius) of the small objective aperture used. ddiff is of the order of typically 0.3e0.5 nm. The kinematical theory of diffraction contrast describes the case of an incoming planar wave and just a single diffracted beam. As the change of the wave amplitude of the diffracted wave is proportional to the amplitude of the primary wave, and total intensity is preserved, it can be shown that the intensity Ig of the diffracted wave oscillates as a function of foil thickness, t, and magnitude of the excitation error, s, in which s ¼ k  k0  g;

n FIGURE 4.3 Sketch of ray diagrams for (A) bright-field and (B,C) dark-field imaging.

(4.3)

112 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

and is given by Ig ¼

 2 2 pt sin ðptseff Þ x ðptseff Þ2

(4.4)

in which the extinction length is x ¼

pV ½lFðqÞ

(4.5)

for unit cell volume V, wavelength l, and structure factor F(q), and the effective excitation error is seff ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s2 þ x2

(4.6a)

Dynamical theory finally yields a damping and an effective extinction length x xeff ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 1 þ s2 x

(4.6b)

Eq. (4.4) describes a periodic oscillation (called Pendellösung) and hence intensity fluctuations as a function of depth in the foil (thickness fringes). Fulfilling the Bragg condition exactly then means s ¼ 0 and gives long oscillations (see Fig. 4.4).

4.3.2.2 Weak-Beam Dark-Field Imaging This method employs imaging with a crystal reflection of type g when the crystal is oriented into a two-beam condition, with the Ewald sphere cutting through 0 and mg, in which m is an integer. Using a weak diffraction spot for

n FIGURE 4.4 Excitation error and Ewald’s sphere construction for the two-beam case.

4.3 Electron Microscopy Methods 113

imaging means very low intensity (several tens of seconds or even several minutes of exposure times are normal) but high contrast, and the images appear sharp with low background, due to a large excitation error s, which puts most of the sample out of contrast [15]. This method was invented to study defects with high strain fields, such as around dislocation, stacking faults, or inclusions [16].

4.3.2.3 High-Resolution Electron Microscopy A larger objective aperture can let several reflections pass. The nondiffracted and diffracted beams interfere, and the resulting interference pattern can be recorded. As with all interference patterns, they are notoriously difficult to interpret by the human eye. If only a strong undiffracted beam (g1 ¼ 0) and one low-order diffracted beam (g2 ¼ ghkl) interfere with each other and the effects of lens aberrations are neglected, the resulting wave is a simple (co)sine wave in real space with period dhkl ¼ 1/ghkl; however, any other condition is much more complex. Consider an incoming wave function of unity amplitude: J0 ¼ 1

(4.7)

Below the specimen, this wave function has been modulated so that its amplitude has decreased by a little amount a and its complex phase been shifted by an angle 4 that both may depend on position r, so Js ðrÞ ¼ 1  aðrÞ þ i4ðrÞ

(4.8a)

Assume the specimen has only a single spatial frequency q along x-direction so that Js ðxÞ ¼ 1  ½a þ i4cosð2pqxÞ

(4.8b)

The microscope now modulates this with a contrast transfer function dominated by spherical aberration constant Cs and focus f: cðgÞ ¼

 p 3 4 Cs l g þ 2f lxg2 2

(4.9)

Then Js ðxÞ ¼ 1  ½a þ i4cosð2pqxÞexpðicÞ.

(4.10)

The measured intensity then is the modulus squared of this wave function:    1 IðxÞ ¼ 1 þ a2 þ 42  2a cosð2pqxÞcos cðqÞ þ 24 cosð2pqxÞsin cðqÞ 2  1 2 þ a þ 42 cosð4pqxÞ. 2 (4.11)

114 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

The first term in square brackets is simply a constant. The amplitude is transferred with cosc and the phase with sinc. The weak-phase object approximation means a z 0 so that only the phase transfer needs to be considered. In case the phase contrast transfer function sinc(q) has a zero for the corresponding spatial frequency q, the third term that contains the spatial modulation of the specimen will vanish. In addition, with the last term, an artificial double frequency (half-spacings) has appeared, yielding fine details in positions where no atoms are at all! Hence, the consensus is to try to image thin specimens that can be treated as weak phase objects, under conditions near the so-called extended Scherzer focus defined as rffiffiffiffiffiffiffiffiffiffiffi 4 lCs 3

fsch ¼ 

(4.12)

which maximizes the passband of uniform phase contrast transfer (PCTF), under which condition atoms and atomic columns always appear dark. In this case, the point resolution of the electron microscope is given as 1

dpoint ¼ ðCs lÞ4

(4.13)

An excellent textbook on the details of contrast theory in lattice imaging is by Spence [17]. The above classic treatment holds for the case of a positive aberration constant (Cs > 0) and underfocus (f < 0). With the recent advent of aberration correctors, the spherical aberration constant can now be set to nearzero values, giving improved resolution, however, potentially reducing or even inverting the contrast. Hence, it is important in aberration-corrected high-resolution electron microscopy (HREM) to work away from the condition Cs ¼ 0, at either small positive Cs (atoms dark in underfocus, bright in overfocus) or small negative Cs (atoms bright in underfocus, dark in overfocus) [19]. The spatial resolution is still dictated by the aberrations of the microscope lenses, and typically 0.1e0.2 nm without aberration correction and 0.05e0.1 nm with aberration correction [20]. The improved quality of lattice images recorded with aberration correction when comparing Figs. 4.6 and 4.7 is obvious.

4.3.2.4 Electron Holography Electron holography directly utilizes the wave nature of electrons to record and analyze specific interference patterns. As a rule, reproducible recording of holographic fringes is experimentally very difficult: the wavelengths of electrons are very short, in the picometer range, so that the fine fringes are to be recorded at extremely high magnifications and are prone to blur and noise due to drift and stray fields. Hence, holography experiments

4.3 Electron Microscopy Methods 115

(A)

(B)

n FIGURE 4.5 (A) Bright-field and (B) (0002) dark field pair of transmission electron microscopy images of ZnO crystal doped with Fe2O3, yielding basal and pyramidal inversion domain boundaries with the arrows in (B) pointing along the c-axes of the hexagonal domains. From T. Walther, F. Wolf, A. Recnik, W. Mader, Quantitative microstructural and spectroscopic investigation of inversion domain boundaries in sintered zinc oxide ceramics doped with iron oxide, Int. J. Mater. Res. 97 (7) (2006) 934e942.

n FIGURE 4.6 Lattice image of a perovskite multilayer. From T. Walther, Spectrum imaging of thin films

of oxides and perovskites, Proceedings of the ICEM-15, vol. 3, Durban, South Africa (2002) 123e124.

116 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

n FIGURE 4.7 Aberration-corrected lattice image of perovskite layers showing a pronounced difference

between cubic SrTiO3 and orthorhombic (La,Ca)MnO3 the larger inplane lattice constant for which is related to the pronounced 0.8-nm spacing observed at the lower interface. From T. Walther, I.M. Ross, Aberration corrected high-resolution transmission and scanning transmission electron microscopy of thin perovskite layers, Phys. Proc. 40 (2013) 49e55.

necessitate an almost ideal laboratory infrastructure, minimizing all possible disturbances, such as mechanical vibrations, temperature gradients, acoustic noise, air movement, magnetic stray fields from earth loops in the electric setup, and 50 Hz AC noise. Once holograms have been successfully recorded, their interpretation is often surprisingly straightforward and elegant [22]. The most widely used electron holographic technique uses a Möllenstedt bi-prism, which is an electrically conducting thin wire charged to several hundreds of volts, placed in an image-conjugate plane (often replacing the selected-area aperture). This wire acts as a beam splitter. Then an image is acquired that contains both the reference wave (in an area without specimen) and the superposition of reference and scattered wave, from which the latter can be recovered in amplitude and phase. The complex phase shift (of an electron wave in real space) can be derived from the action of the Lorentz force F ¼ eðE þ v  BÞ

(4.14)

on an electron of elementary charge e and relativistic speed v v ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi eUc2 ðeU þ 2m0 c2 Þ ðeU þ m0 c2 Þ

(4.15)

4.3 Electron Microscopy Methods 117

in which U is the acceleration voltage, c the speed of light, m0 the electron rest mass, E the electric field, and B the magnetic field vector. This yields for the phase shift 4ðrÞ ¼

e Zv

Z VðrÞdz 

e Z

Z AðrÞdr

(4.16)

in which V(r) is the projected electric potential that needs to be integrated along beam direction z and A(r) the magnetic vector potential, which needs to be evaluated so that the integral represents the enclosed magnetic flux. The electric potential term includes contributions from the mean inner potential, deviations thereof as induced by charged crystal defects or by strain fields, doping, polarization, etc. [23]. The shift of lattice fringes of period g is then related to real-space displacements Dr by fðr Þ ¼ 2pDrg

(4.17)

So, the phase and thereby the previous potentials can be extracted with high precision. A review article that describes various methods of inline and offaxis holography has been written some 20 years ago [24]. More recently, some electron microscopes have been constructed with multiple biprisms that can interfere many different beams to measure components of displacement fields in various directions simultaneously [25].

4.3.2.5 Energy-Filtered Transmission Electron Microscopy A magnetic field perpendicular to an electron beam will deflect electrons according to the Lorentz force, thereby separating them according to energy [see the section on electron energy-loss spectroscopy (EELS)]. If the electron microscope has an imaging energy filter (either incolumn U-type or postcolumn single-prism type), then a slit inserted in the energydispersive plane selects electrons that have undergone a specific energy loss. Imaging with these contains element-specific information if the slit is located just behind a characteristic ionization edge of an element. High nonspecific background exists underneath each energy-loss edge (cf. section on spectroscopy methods later). The contribution of this background can be suppressed by jump-ratio imaging (i.e., dividing a post-edge image by a pre-edge image, [26]) or three-window elemental mapping (i.e., subtracting from a post-edge image the background intensity extrapolated from two or more pre-edge images acquired at slightly different energies [27]). Suppression of diffraction contrast can be achieved by division by a zero-loss filtered image or rocking-beam illumination [28] or, better still, by recording a whole series of energy-filtered pre- and post-edge images and performing a linear least squares fit removal of the background (see Fig. 4.8) [29]. Such

118 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

20 nm

<0

0 – 0.1

0.1 – 0.2

0.2 – 0.3

0.3 – 0.4

0.4 – 0.5

0.5 – 0.6

0.6 – 0.7

n FIGURE 4.8 Quantitative x(In) concentration map through an InxGa1xAs/GaAs island. From T. Walther, A.G. Cullis, D.J. Norris, M. Hopkinson, Nature of the Stranski-Krastanow transition during epitaxy of InGaAs on GaAs, Phys. Rev. Lett. 86 (11) (2001) 2381e2384.

elemental maps show the distribution of chemical elements in the sample, and if elemental maps of all relevant elements are acquired, then compositional concentration maps can be calculated from their ratios by dividing the elemental maps by the corresponding scattering cross-sections [30]. The spatial resolution achievable by this technique is mainly given by the chromatic aberration if the slit width is large. However, it is often dominated in practice by the need to cross correlate several images drifted relative to each other during longer exposure times and differing in contrast (if there is a strong contrast reversal across the edge, this implies a strong chemical signal but more problems with cross-correlation!).

4.3.2.6 Annular Dark-Field and Annular Bright-Field Scanning Transmission Electron Microscopy Scanning transmission electron microscopy (STEM) employs a focused probe, which can be obtained by strong common excitation of condenser and objective lenses. In the ideal case, the specimen sits midway between the pole pieces of upper and lower objective lenses that are both equally excited such that the electron beam forms an X-like crossover in the specimen plane. The beam is then deflected and scanned point by point in a raster mode over the specimen surface, and deflection coils below the specimen act synchronously to compensate the induced tilt to retain only the lateral-shift component of the movement. This works well at high magnifications, at which the scanned areas are small, but at lower magnifications, at which the scanned areas are large, even small relative misalignments of the scan and the descan coils often become apparent in form of a jitter of the diffraction pattern, i.e., residual tilts not being perfectly compensated. Hence, fine beam alignment is performed for a stationary probe with the help of so-called ronchigrams, i.e., defocused-

4.3 Electron Microscopy Methods 119

shadow images of the probe in the back focal plane, while the scan coils are switched off [31]. Only after the beam is aligned with the optic axis and compensation of astigmatism and coma, scanning is resumed. At each point, a variety of signals can be collected. If a small detector is placed on axis, this records the bright-field intensity and yields images similar to BF TEM images (albeit recorded at higher convergence). A ring detector that integrates the intensity scattered sideways over a larger angular range yields an annular dark-field (ADF) image, which differs from classical DF TEM in that the ADF intensity no longer includes a single diffraction spot but an azimuthal integral over all diffraction spots and diffusely scattered intensity of the same distance from the optic axis (see Figs. 4.9 and 4.10). Hence, diffraction contrast is suppressed. At very short camera lengths, the range of collection angles can become very large and comprise intensity scattered further out than any diffraction disk is visible. In this case of so-called high-angle ADF (HAADF), the differential elastic scattering cross-section for Rutherford scattering of a single atom is 2 4 2

4g l Z dselastic ðqÞ ¼ h  2 i dU 2 a0 q2 þ q20

(4.18)

in which

n FIGURE 4.9 Annular dark-field scanning transmission electron microscopy image of SiGe/Si multiple quantum wells in which the camera length was reduced successively during the recording from top to bottom. The inner collection angle of the ring detector is inversely related to the camera length. The intensity is reduced but the contrast increased for larger angles. From T. Walther, A new experimental procedure to quantify annular dark field images in scanning transmission electron microscopy, J. Microsc. 221 (2) (2006) 137e144.

120 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

n FIGURE 4.10 Annular dark-field scanning transmission electron microscopy image of perovskite multilayers similar to those in Fig. 4.6 but with calcium instead of barium. Z-contrast means columns of heavy La3þ ions in the La2/3Ca1/3MnO3 layers stand out bright, and, in the thinnest layer, an atomic step can be clearly seen. From T. Walther, E. Quandt, H. Stegmann, A. Thesen, G. Benner, First experimental test of a new monochromated and aberration-corrected 200kV field-emission scanning transmission electron microscope, Ultramicroscopy 106 (11e12) (2006) 963e969.

1 g ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  ðv=cÞ2

(4.19)

is a relativistic factor, l the wavelength, Z the atomic number, a0 ¼ 0.053 nm the Bohr radius, q the scattering angle, q0 ¼ l/r0, and r0 describes the radius of a screened nuclear potential. The total scattered intensity is then given by summation over the range of collection angles and over all atoms in the sample. The total intensity would be approximately linear in thickness and increases quadratically with the average atomic number, Z. This explains why high-angle ADF is often referred to as “Z-contrast” [32]. Strain and diffraction contrast then are very strongly suppressed compared to BF and medium-angle ADF conditions; however, near-zone axis orientations being necessary for atomic column-resolution ADF contrast, strain can still be observed even for very large angles >200 mrad [33].

4.3.3 Spectroscopy Methods 4.3.3.1 Energy-Dispersive X-ray Spectroscopy If the electron beam hits a bound inner-shell electron of an atom, it can ionize the atom. This creates an empty electron state (hole) in the ionized

4.3 Electron Microscopy Methods 121

n FIGURE 4.11 Energy-dispersive X-ray spectrum of an InGaAs specimen, glued to a copper grid. Note X-rays are detected from C, Al (labeled Si), and Cu all

of which stem from the polymerized glue and the metal grid several micrometers away from the point of analysis.

n FIGURE 4.12 Energy-dispersive X-ray maps of coreeshell nanoparticles with w4 nm Pt cores and large Fe2O3 shells, all dispersed on C film. The maps display background-subtracted net counts of the corresponding lines.

atom that can be filled by an electron from a higher shell jumping into the energetically lower inner shell. The difference in shell energies can be radiated in the form of a photon, which in most cases will be an X-ray (see Figs. 4.11 and 4.12). The X-ray lines are named after the shell of the final (lower) state, e.g., a transition from an L- to a K-shell would be termed a Ka-line [12]. Solid-state X-ray detectors can be used to detect such X-rays. According to the material, one distinguishes Si:Li detectors (drifting

122 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

Li ions through several-millimeters-thick silicon purifies the material in that the Li ions sweep with them all point defects), high-purity Ge detectors, or silicon-based solid-state detectors (SSD). The latter ones is thinner, no longer requires cooling to liquid nitrogen temperatures, achieves higher count rates (as they have multiple-ring anodes, and so can detect electrone hole pairs at shorter diffusion times) but have the disadvantage that their smaller thickness of w0.4 mm means very hard X-rays can go through them without being detected. All detectors can be operated with a thin polymer window in front to shield the cooled detector from the (not perfect) vacuum around the specimen, which could cause condensation of water and the resulting ice reducing the detector sensitivity, or windowless. An X-ray is detected and identified based on the number of electronehole pairs it produces in the reversed-biased diode made of the semiconductor. Therefore, in principle, only a single X-ray can be detected at any time (two simultaneous X-rays of 1.5 keV would be indistinguishable from one 3keV X-ray). This means the detector will have to be read out at high speed (lifetimes in the microsecond range are typical), and during its readout (called “dead time”) it will not register any new counts. The dead time for most detectors should not lie above 50% of the total acquisition time (¼ life time þ dead time) to guarantee correct processing of the spectrum by the multichannel analyzer, which identifies and corrects for sum and escape peaks automatically. As the nonspecific background only comprises the strobe peak at 0 eV and a continuous X-ray band from decelerated electrons, an energy-dispersive X-ray spectrum consists of discrete peaks (“lines”) on top of a low background, so programs can identify and quantify their net counts routinely. The advantage of automation, ease of quantification, and also the wide range of excitations [lines up to w80 keV can be detected in (S)TEM] contrasts with the disadvantages of low detection probabilities (the emission is isotropic, and small collection angles in the range of 0.12e1.6 mrad correspond to 1e13% of the whole 4p sphere). Poor energy resolution can complicate the separation of peak overlaps. Most manufacturers quote the full width at half maximum (FWHM) of the Mn Ka line as spectral resolution, which lies in the range of 120e140 eVd at lower energies the lines can be narrower, typically 40e60 eV wide. In summary, energy-dispersive X-ray spectroscopy (EDXS) is most useful to detect and quantify K and L lines in the range of 1e10 keV, which means that elements with atomic numbers Z > 11 can be detected and quantified. More details can be found in Ref. [36].

4.3.3.2 Electron Energy-Loss Spectroscopy X-ray production (and its radiationless alternative, Auger electron ejection) is a secondary process after the initial ionization has taken place. In this

4.3 Electron Microscopy Methods 123

ionization, the primary (fast) electron transfers energy to a secondary (bound) electron to excite it from a shell close to an atomic nucleus into a higher shell further away from the nucleus. The primary electron will thus itself lose energy equivalent to the sum of the ionization threshold energy plus any kinetic energy it can transfer to the secondary electron. As a result, the electron energy-loss spectrum contains ionization coreloss edges with a sharp onset that decay asymptotically into the secondary electron background (see Figs. 4.13 and 4.14). After the zero-loss peak (including unscattered and phonon-scattered electrons), EELS can also contain intra- and interband transitions if the bonding is not metallic (in the range 0.1e3 eV for semiconductors and 3e8 eV for insulators), surface and bulk plasmons (in the range 1e30 eV), and multiple plasmon peaks (if the specimen is thick enough to yield multiple inelastic scattering). Multiple plasmon transitions obey Poisson statistics, so that for energies larger than w5EP, the background decays almost exponentially. Hence, ideal edges for quantification are those in the energy range of typically 0.1e2 keV. Below w100 eV, the background fitting and subtraction can be prone to large systematic errors. Above w2000 eV, the ionization cross-sections are getting so small that large statistical errors are encountered even when multiple exposures and large integration windows are employed. Therefore,

(A)

(B)

(C)

(D)

(E)

n FIGURE 4.13 (A) Electron energy-loss spectroscopy of slightly oxidized FeNi nanoparticles with the background subtraction for OK, FeL, and NiL edges indicated. (B) Bright-field image, and (CeE) energy-filtered transmission electron microscopy elemental maps of (C) O, (D) Fe, and (E) Ni showing most particles are FeNi alloys with some surface oxide; the particle in the center is pure Ni with a NiO shell.

124 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

n FIGURE 4.14 Electron energy-loss near-edge structure (ELNES) of different manganese oxides,

measured with a monochromated 200-kV electron microscope at 0.17 eV (FWHM) energy resolution. From T. Walther, H. Schmid, H. Stegmann, Electron energy-loss spectroscopy at 0.1e0.2eV resolution in a new monochromatic and aberration-corrected 200kV field-emission scanning transmission electron microscope, Proceedings of the ICM-16, Sapporo, Japan, vol. 2 (2006) 833.

EELS is ideally suited for qualitative and quantitative analysis of light elements (K-edges for 3 < Z < 15, L-edges for 15 < Z < 39, M-edges for 36 < Z < 77). Due to plural plasmon scattering and the need to extract ideally single scattering contributions, there exists an ideal thickness for EELS given by the inelastic mean free path L. For most materials and typical medium-voltage electron microscopes, values for L lie in the range of 50e150 nm, and ideal specimen thicknesses in the range of 0.2e0.5L. Then the spectrum will be dominated by the single scattering contribution. For larger thicknesses, the experimental EELS should be deconvoluted by the low-loss spectral component to yield consistent single scattering contributions that can be compared and quantified easily. In addition to compositional analysis, the high-energy resolution obtained (in the range of 0.3e1 eV without and 0.02e0.2 eV with monochromator) also allows electronic properties to be extracted directly from the low-loss region: via KramerseKronig transform, the real and imaginary parts of the dielectric function, and thus the refractive index and the absorptive index can be calculated. In addition, “finger-printing” of the bonding environment of specific atoms is possible based on comparing the energy-loss near-edge structures of K- and L-edges. The L3/L2 ratios, for example, yield the valence of transition metal ions within compounds. All this is explained in great mathematical detail in the seminal EELS textbook by Egerton [37].

4.4 Applications to Nanostructures 125

4.3.3.3 Cathodoluminescence Spectroscopy If a light-sensitive detector is incorporated near the sample, then panchromatic cathodoluminescene maps can be extracted, which appear bright where the electron beam generates transitions that can decay radiatively by the emission of infrared, visible, or ultraviolet light. If an optical spectrometer is incorporated with good coupling efficiency (via a retractable ellipsoidal [39] or parabolic [40] mirror with a hole for the electron beam or an optical fiber close to the scanned region [41], either of which can guide the light emitted to the attached spectrometer), then optical spectroscopy and mapping can be applied. This is useful for investigating optical transitions in semiconductor structures or plasmons in metallic nanostructures. The spatial resolution attainable will depend on the specimen material and the sample geometry; in the SEM 20nm-thin GaAs quantum wells have been resolved in a CL map [42], and in the TEM w5nm periods in GaN/AlN quantum well stacks [43].

4.4 APPLICATIONS TO NANOSTRUCTURES 4.4.1 Defects in Bulk Materials Zero-dimensional (point) defects are rather difficult and often impossible to investigate in TEM- or STEM-based experiments, as this would necessitate atomic column resolution and at the same time a signal-to-noise ratio high enough to visualize single-atom exchanges or vacancies. Although such studies do exist [44e47], they are confined to specific systems often chosen for demonstration purposes (heavy atoms in weakly scattering materials) rather than technological importance. One-dimensional lattice defects, i.e., extended defects such as dislocations, are ideally investigated by HREM or BF/DF TEM (in which the latter visualizes the strain field around the dislocations rather than the dislocation cores themselves). Twodimensional lattice defects, such as stacking faults, twins, antiphase, or inversion-domain boundaries, can also be successfully imaged with atomic resolution by HREM or HR-STEM; however, the field of view then is rather limited. An elegant technique, and in terms of representativeness sometimes more useful, is DF imaging of the individual domains with Bragg reflections that are typical of the corresponding domains, i.e., (111) versus (1e11) for twins in face-centered cubic (fcc) materials and (0002) versus (000e2) for inversion domains in hexagonal close-packed (hcp) materials, such as in Figs. 4.5 and 4.15, or centered on reflections that are kinematically forbidden in the bulk and only occur at domain boundaries due to the defects.

126 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

(B)

(A)

50 nm

2nm

n FIGURE 4.15 Annular dark-field scanning transmission electron microscopy of inversion domain boundaries on (0001) basal planes in Fe-doped ZnO crystal. From T. Walther, F. Wolf, A. Recnik, W. Mader, Quantitative microstructural and spectroscopic investigation of inversion domain boundaries in sintered zinc oxide ceramics doped with iron oxide, Int. J. Mater. Res. 97 (7) (2006) 934e942.

4.4.2 Thin Films and Quantum Wells The most widespread application of TEM- and STEM-based techniques in nanotechnology often is to measure layer thicknesses and local deviations thereof to high accuracy. For this, thin films or quantum wells need to be imaged edge-on, which is not a problem if they are grown on a singlecrystalline substrate, the Bragg reflections of which can be used to tilt the specimen onto a suitable zone axis or two-beam condition. BF or DF images have a resolution on the order of 0.3e0.5 nm, given by the diffraction limit imposed by the objective aperture used. However, the FWHM of thin layers depends less on resolution but more on the precise diffraction condition (which determines the contrast of the layers and thus also their apparent widths) and the magnification calibration. Electromagnetic lenses typically lead to hysteresis and, without precise calibration, the nominal values given by the instrument manufacturers are hardly better than 5% relative. The latter also applies to BF, ABF, and annular dark-field scanning transmission electron microscopy (ADF STEM) images without lattice resolution. If some known lattice planes are resolved, this can serve as an inherent magnification calibration. The position of interfaces can then be determined on the atomic scale (Fig. 4.16); however, due to defocusing effects all but the ADF technique usually give a delocalization of about one atomic monolayer, so thicknesses (¼lateral distances between adjacent interfaces) are subject to errors of typically 2 monolayers. This sounds small but will be larger than the abovementioned 5% for layer widths smaller than 40 atomic planes. Therefore, it is advisable to apply and compare different techniques, ideally TEM and STEM based, when layer widths or nanoparticle diameters need to be determined to high accuracy, as in Fig. 4.18.

4.4 Applications to Nanostructures 127

n FIGURE 4.16 Lattice image of a gate oxide stack in a field-effect transistor [48].

(A)

(B)

2 µm

2 1/nm

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5 nm

n FIGURE 4.17 GaAs nanowires. (A) Annular dark-field scanning transmission electron microscopy overview, (B) selected-area electron diffraction in which

Bragg reflections due to both twin variants are marked by circles/squares, (C) HREM lattice image shows dense stacking faults, which induce {111} faceting of the side surface. From T. Walther, A.B. Krysa, Twinning in GaAs nanowires on patterned GaAs(111)B, Cryst. Res. Technol. 50 (1) (2015) 62e68.

4.4.3 Nanowires Nanowires have the advantage that their needle-like shape often makes any complicated specimen preparation unnecessary. They can be isolated from solutions by putting a drop of the liquid onto a holey carbon film using a micropipette, or they can be harvested from solid substrates by scraping them off with a sharp razor blade and then put onto a holey carbon film.

128 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

(A)

(B)

(C)

n FIGURE 4.18 Determination of Co nanoparticle size from (A) annular dark field (ADF), and (B) HREM, (C) comparison of histograms yields average diameters of 7.15  1.24 nm (ADF of 77 particles) versus 7.17  0.87 nm (HREM of 80 particles). Bright field imaging (not shown) of 111 particles gave 7.12  1.09 nm [54].

Nanowires thinner than about 100 nm can be imaged directly and histograms of lengths and widths obtained easily, although it should be taken into account that the mechanical harvest technique often tends to break nanowires of a high aspect ratio, and the broken parts will always tend to underestimate the true nanowire length. Using HREM or high-resolution scanning transmission electron microscopy (HR-STEM), lattice images can be recorded easily that allow the user to determine the crystal lattice and view stacking faults. The latter ones is quite common in many semiconductors in which fcc and hcp lattices are almost equally stable and stacking faults locally revert the lattice from one to the other type, as in Fig. 4.17. In addition, the nanowire tops (showing distinctive caps if grown from a metal catalyst source) and sidewalls (revealing either clean, facetted, or amorphous surface structures in perspective) can be imaged and studied separately. Only if nanowires are grown on single crystalline substrates and the initial stages of nucleation and growth are to be investigated will it be necessary to make a cross-sectional sample in the standard way to investigate the substrate/nanowire interface. For this, it is often best to embed the nanowires in thin epoxy glue first, then glue a protective wafer piece on top and cut the whole stack along the desired direction before mechanical grinding, polishing, and ion milling the cross-section.

4.4.4 The Problem of Reliable Size Measurements of Nanoparticles and Quantum Dots in Transmission Although electron microscopy is a standard tool to measure size distributions of colloidal and epitaxial quantum dot systems, the microscopist should be aware of potential pitfalls related to the above imaging, mapping,

4.4 Applications to Nanostructures 129

or diffraction methods. TEM-based mapping approaches based on CL, EELS, or EDXS spectral data sets are only meaningful if both statistically significant count rates are obtained and an appropriate sampling (i.e., fine enough pixel size of sampling) is chosen for the maps. For a given dose, both criteria compete with each other, which means that long acquisition times will be needed that may finally induce drift or lead to beam damage or even particle disintegration. Using the EFTEM approach, it has been shown for the example of gold nanoparticles on titania support that the particle detection limit of w1 nm was ultimately limited by surface diffusion of the small particles on the support during the investigation, rather than by electron optics [50]. More recently, aberration-corrected imaging in STEM has confirmed the high surface diffusivity of single metal atoms on top of thin supports, partly driven by electron irradiation [51]. HREM and HR-STEM can both yield atomic resolution images, but the detection probabilities for small colloidal particles will depend very much on the medium of support and the chemistry of the particles themselves. Although particles with diameters >>2 nm yield sufficient phase contrast and are generally well visible, smaller particles will be more difficult to detect under bright-field conditions, which can be due to geometrical overlap problems [52] or their weak scattering relative to polycrystalline supports or other uneven background conditions [53]. If one carefully compares size measurements by HREM and ADF-STEM, then the results for particles >5 nm in diameter typically agree very well, whereas similar measurements for smaller particles can disagree significantly. HREM tends to overlook some of the particles <2 nm in diameter (if tiny crystals are oriented off Bragg conditions, or the particles are amorphous, their phase contrast can be minute), and this will distort the apparent size distribution [54]. In summary, TEM can yield accurate particle-size distributions, but the histograms may be somewhat truncated for particle diameters <2 nm in case of weakly scattering objects or due to beam damage, surface diffusion during extended exposures or simple detection issues. Finally, it should be noted that most nanoparticles are often facetted cuboctahedra, icosahedra, or dodecahedra, with twins and facets that can be imaged directly, which is important for catalytic and optoelectronic applications. Care, however, must be taken with regard to two aspects: first, the imaging electron beam can impart sufficient energy to the atoms to displace them (knock-on damage, which occurs first and foremost at free surfaces in which atoms have fewer bonds to neighbor atoms anchoring them into the lattice). Second, lattice planes can apparently shift near surfaces both due to surface strain effects but also due to the decrease of the specimen thickness in projection, which can only be separated in influence using image simulations.

130 CHAPTER 4 Transmission Electron Microscopy of Nanostructures

4.5 TOMOGRAPHY AND THE PROJECTION PROBLEM All measurements of any structures in transmission geometry are thickness-integrated projections. For electron-beam channeling [55] or for highly focused electron probes with small depths of focus [56], contributions from sections at different depths in the sample may not be weighted equally. This is generally not a problem for colloidal quantum dots as long as they are dispersed evenly on a suitable carbonaceous support grid so that each quantum dot can be imaged individually. On the other hand, problems in interpreting data from buried structures cross-sectioned at unknown sample depths can be significant: the chemical composition, and sometimes even the atomic structure along the electron beam direction, is no longer constant along the electron beam path. In particular, the situation in which epitaxial quantum dots are more or less completely surrounded by other material, which will broaden the electron beam by multiple (mainly elastic) scattering and thereby increase the interaction volume, makes it difficult to assess quantitatively the concentrations of chemical elements within such dots. Raw measurements hence often drastically underestimate concentrations of minority elements [57], and a detailed modeling of the electron beamesolid interaction will be required to reconcile experiment and theory [58]. In such cases, tomographic approaches, or simple projections from different directions near major zone axes, may help to elucidate the complex relationship between shape, lattice structure, strain, and local composition.

4.6 SUMMARY TEM and STEM are powerful and indispensable techniques for the study of nanostructures, because they are unique in providing atomic resolution images and maps that are not typical of the surface (such as most scanning probe methods, some of which can also obtain lateral atomic resolution) but of the bulk, due to the transmission geometry. The interpretation of (S)TEM data can be complex due to the strong interaction of electrons with matter, giving rise to dynamical diffraction effects that can usually be neglected in scattering experiments involving X-rays from highvoltage cathode tubes or synchrotron sources.

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